Bottom Line:
The perievent time histogram (PETH) examines how, on average, neural firing modulates before and after the alignment event.This is used to generate a probability distribution of the event occurrence, using Bayes' rule.By an information theoretic approach, this method yields a single value (in bits) that quantifies the reduction in uncertainty regarding the time of an external event following observation of the spike train.

ABSTRACTSingle-neuron firing is often analyzed relative to an external event, such as successful task performance or the delivery of a stimulus. The perievent time histogram (PETH) examines how, on average, neural firing modulates before and after the alignment event. However, the PETH contains no information about the single-trial reliability of the neural response, which is important from the perspective of a target neuron. In this study, we propose the concept of using the neural activity to predict the timing of the occurrence of an event, as opposed to using the event to predict the neural response. We first estimate the likelihood of an observed spike train, under the assumption that it was generated by an inhomogeneous gamma process with rate profile similar to the PETH shifted by a small time. This is used to generate a probability distribution of the event occurrence, using Bayes' rule. By an information theoretic approach, this method yields a single value (in bits) that quantifies the reduction in uncertainty regarding the time of an external event following observation of the spike train. We show that the approach is sensitive to the amplitude of a response, to the level of baseline firing, and to the consistency of a response between trials, all of which are factors that will influence a neuron's ability to code for the time of the event. The technique can provide a useful means not only of determining which of several behavioral events a cell encodes best, but also of permitting objective comparison of different cell populations.

f5: Bias estimation. A: raster plot of neuron activity. B: raster plot of neuron shown in A after random shuffling of the ISIs. C: single trial and mean shift likelihood distributions for shuffled data. D: distribution of information values calculated from 100 random shuffles. The dotted line shows the information value calculated from the original raster plot in A.

Mentions:
To estimate a P < 0.05 significance level for the measured information about event timing, a shuffled data set (Fig. 5B) was generated from the original data (Fig. 5A). The ISIs of each trial were shuffled; the first spike was chosen randomly so that(10)\documentclass[10pt]{article}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{pmc}\usepackage[Euler]{upgreek}\pagestyle{empty}\oddsidemargin -1.0in\begin{document}\begin{equation*}0{\leq}ISI_{0}^{\prime}{\leq}ISI_{0}+ISI_{last}\end{equation*}\end{document} where ISI′0 is the first incomplete interval of the shuffled trial and ISI0 and ISIlast are the first and last incomplete intervals of the real trial (“incomplete intervals” are the ISIs that fell only partially within the timeframe of the actual trial, i.e., the time period before the first spike and after the last).

f5: Bias estimation. A: raster plot of neuron activity. B: raster plot of neuron shown in A after random shuffling of the ISIs. C: single trial and mean shift likelihood distributions for shuffled data. D: distribution of information values calculated from 100 random shuffles. The dotted line shows the information value calculated from the original raster plot in A.

Mentions:
To estimate a P < 0.05 significance level for the measured information about event timing, a shuffled data set (Fig. 5B) was generated from the original data (Fig. 5A). The ISIs of each trial were shuffled; the first spike was chosen randomly so that(10)\documentclass[10pt]{article}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{pmc}\usepackage[Euler]{upgreek}\pagestyle{empty}\oddsidemargin -1.0in\begin{document}\begin{equation*}0{\leq}ISI_{0}^{\prime}{\leq}ISI_{0}+ISI_{last}\end{equation*}\end{document} where ISI′0 is the first incomplete interval of the shuffled trial and ISI0 and ISIlast are the first and last incomplete intervals of the real trial (“incomplete intervals” are the ISIs that fell only partially within the timeframe of the actual trial, i.e., the time period before the first spike and after the last).

Bottom Line:
The perievent time histogram (PETH) examines how, on average, neural firing modulates before and after the alignment event.This is used to generate a probability distribution of the event occurrence, using Bayes' rule.By an information theoretic approach, this method yields a single value (in bits) that quantifies the reduction in uncertainty regarding the time of an external event following observation of the spike train.

ABSTRACTSingle-neuron firing is often analyzed relative to an external event, such as successful task performance or the delivery of a stimulus. The perievent time histogram (PETH) examines how, on average, neural firing modulates before and after the alignment event. However, the PETH contains no information about the single-trial reliability of the neural response, which is important from the perspective of a target neuron. In this study, we propose the concept of using the neural activity to predict the timing of the occurrence of an event, as opposed to using the event to predict the neural response. We first estimate the likelihood of an observed spike train, under the assumption that it was generated by an inhomogeneous gamma process with rate profile similar to the PETH shifted by a small time. This is used to generate a probability distribution of the event occurrence, using Bayes' rule. By an information theoretic approach, this method yields a single value (in bits) that quantifies the reduction in uncertainty regarding the time of an external event following observation of the spike train. We show that the approach is sensitive to the amplitude of a response, to the level of baseline firing, and to the consistency of a response between trials, all of which are factors that will influence a neuron's ability to code for the time of the event. The technique can provide a useful means not only of determining which of several behavioral events a cell encodes best, but also of permitting objective comparison of different cell populations.